Multiply the following complex numbers: $({5-5i}) \cdot ({-1+5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-5i}) \cdot ({-1+5i}) = $ $ ({5} \cdot {-1}) + ({5} \cdot {5}i) + ({-5}i \cdot {-1}) + ({-5}i \cdot {5}i) $ Then simplify the terms: $ (-5) + (25i) + (5i) + (-25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -5 + (25 + 5)i - 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -5 + (25 + 5)i - (-25) $ The result is simplified: $ (-5 + 25) + (30i) = 20+30i $